Question

Entering your solution Please note that the system should accept any correct answers, but it is very strict about it: you can only apply one law per step, not more (note that this also includes the fact that you cannot apply the same law twice in one go - it has to be done in two steps: it is one law per step, not one type of law per step). The checker should tell you when it thinks that you entered more than one law. It is not possible to reveal the solution: checking the solution automatically is easier than computing the solution. You may copy-paste the expression in the first box: ((q^p) V-p) ^-p Select the number of steps you need: 3 LHSE III =

Answer 1

LHS = $((q \wedge p) \vee \neg p) \wedge \neg p$

=> Distributive law

(de v d) A (dl v (dvb))

=> $((q \wedge p) \wedge \neg p) \vee \neg p$   Idempotent law

=> $(q \wedge (p \wedge \neg p)) \vee \neg p$ Associative law

=> $(q \wedge 0) \vee \neg p$ Complementarity law

=> $0 \vee \neg p$   Annulment

=> $\neg p$ Identity